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arafune committed Feb 26, 2024
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5 changes: 3 additions & 2 deletions docs/source/dev-guide.rst
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Expand Up @@ -7,15 +7,16 @@ Topics
Installing an editable copy of PyARPES
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

1. Install `rye <https://rye-up.com/> to make an isolated environment for development.
1. Install `rye <https://rye-up.com/>` to make an isolated environment for development.
2. Clone the respository

.. code:: bash
git clone https://gitlab.com/arafune/arpes
3. Install libraries to develop PyARPES with
``rye sync``

``rye sync``.

4. After that, activate the .venv/ environment.

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27 changes: 23 additions & 4 deletions docs/source/single-particle-spectral.rst
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Expand Up @@ -20,16 +20,35 @@ disentangle, it is typically slowly varying in momentum and photon
energy, and therefore ARPES can be thought of as measuring also
:math:`A(\textbf{k}, \omega)`.

.. math::


.. only:: html

.. math::
\textbf{A}(\mathbf{k}, \omega) = -\frac{1}{\pi}
\frac{\color{blue}{\Sigma''(\color{black}{\mathbf{k}, \omega})}}
{[\omega - \hspace{-0.25em}\underbrace{\color{green}{\epsilon_0(\color{black}{\mathbf{k}})}}_{\color{green}{\text{Bare band}}}\hspace{-0.25em} - \hspace{-0.4em}\underbrace{\color{red}{\Sigma'\left(\color{black}{\mathbf{k},\omega}\right)}}_{\color{red}{\text{E-renormalization}}}\hspace{-0.9em}]^2 +
[\underbrace{\color{blue}{\Sigma''\left(\color{black}{\mathbf{k},\omega}\right)}}_{
\frac{\color{blue}{\Sigma''\color{white}({\mathbf{k}, \omega})}}
{[\omega - \hspace{-0.25em}\underbrace{\color{green}{\epsilon_0\color{white}({\mathbf{k}})}}_{\color{green}{\text{Bare band}}}\hspace{-0.25em} - \hspace{-0.4em}\underbrace{\color{red}{\Sigma'\color{white}\left({\mathbf{k},\omega}\right)}}_{\color{red}{\text{E-renormalization}}}\hspace{-0.9em}]^2 +
[\underbrace{\color{blue}{\Sigma''\color{white}\left({\mathbf{k},\omega}\right)}}_{
\color{blue}{\text{Lifetimes}}
}]^2}
.. only:: not html

.. math::
\textbf{A}(\mathbf{k}, \omega) = -\frac{1}{\pi}
\frac{\color{blue}{\Sigma''(\color{black}{\mathbf{k}, \omega})}}
{[\omega - \hspace{-0.25em}\underbrace{\color{green}{\epsilon_0\color{black}({\mathbf{k}})}}_{\color{green}{\text{Bare band}}}\hspace{-0.25em} - \hspace{-0.4em}\underbrace{\color{red}{\Sigma'\color{black}\left({\mathbf{k},\omega}\right)}}_{\color{red}{\text{E-renormalization}}}\hspace{-0.9em}]^2 +
[\underbrace{\color{blue}{\Sigma''\color{black}\left({\mathbf{k},\omega}\right)}}_{
\color{blue}{\text{Lifetimes}}
}]^2}
From this quantity much can be extracted, including single-particle band
structure, energy renormalization by interaction, and measurement of the
quasiparticle lifetimes. ARPES therefore makes available momentum
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